%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:12:56 AM UTC 2026
% Result : Theorem 28.38s 14.05s
% Output : CNFRefutation 28.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 27 unt; 2 def)
% Number of atoms : 238 ( 146 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 235 ( 82 ~; 110 |; 31 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 10 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(m_MulUnit,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mZeroMul,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ) ).
fof(mDefDiv,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ).
fof(mDefQuot,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( sdtpldt0(xm,X0) = xp
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xn != xp ) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ) ).
fof(m__,conjecture,
( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c11,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c12,plain,
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c23,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| X1 = sz00
| X0 = sz00 ),
inference(clausification,[status(esa)],[mZeroMul]) ).
cnf(c48,plain,
( X1 = sdtasdt0(X0,sK61(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c51,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
cnf(c70,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c89,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c91,plain,
( ~ aNaturalNumber0(X0)
| xp != sdtasdt0(X0,X1)
| X0 = xp
| ~ aNaturalNumber0(X1)
| X0 = sz10 ),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c94,plain,
aNaturalNumber0(sK99),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c95,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK99),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c96,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c101,plain,
xn != xp,
inference(clausification,[status(esa)],[m__2287]) ).
cnf(c110,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c111,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c112,plain,
( xk = sz10
| xk = sz00 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c113,plain,
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c115,plain,
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[status(thm)],[c12,c71]) ).
cnf(d1,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c13,c72]) ).
cnf(d2,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,sK99),
inference(demodulation,[status(thm)],[c95,c110]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xn = sz00
| xm = sz00
| sdtasdt0(xp,sK99) != sz00 ),
inference(superposition,[status(thm)],[c95,c23]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xm = sz00
| xn = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xm)
| xm = sz00
| xn = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(resolution,[status(thm)],[c70,d4]) ).
cnf(d6,plain,
( xm = sz00
| xn = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(resolution,[status(thm)],[c71,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sz00)
| xm != sz00 ),
inference(superposition,[status(thm)],[d1,c115]) ).
cnf(d8,plain,
xm != sz00,
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( xn = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sz00)
| xn != sz00 ),
inference(superposition,[status(thm)],[d1,c113]) ).
cnf(d11,plain,
xn != sz00,
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
sdtasdt0(xp,xk) != sz00,
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xn = xp
| xn = sz10
| xp != sdtasdt0(xp,sK99) ),
inference(superposition,[status(thm)],[c95,c91]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xp != sdtasdt0(xp,xk)
| xn = xp
| xn = sz10 ),
inference(demodulation,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(xm)
| xp != sdtasdt0(xp,xk)
| xn = xp
| xn = sz10 ),
inference(resolution,[status(thm)],[c70,d14]) ).
cnf(d16,plain,
( xp != sdtasdt0(xp,xk)
| xn = xp
| xn = sz10 ),
inference(resolution,[status(thm)],[c71,d15]) ).
cnf(d17,plain,
( xp != sdtasdt0(xp,xk)
| xn = sz10 ),
inference(resolution,[status(thm)],[c101,d16]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,sK61(xp,sdtasdt0(xn,xm))) ),
inference(resolution,[status(thm)],[c48,c96]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xn,xm))) ),
inference(demodulation,[status(thm)],[d18,c110]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xp,xk))) ),
inference(demodulation,[status(thm)],[d19,c110]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xp,xk))) ),
inference(demodulation,[status(thm)],[d20,c110]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xp,xk))) ),
inference(resolution,[status(thm)],[c72,d21]) ).
cnf(d23,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[c11,c72]) ).
cnf(d24,plain,
xk = sdtsldt0(sdtasdt0(xp,xk),xp),
inference(demodulation,[status(thm)],[c111,c110]) ).
cnf(d25,plain,
( xk = sz00
| xk = sdtsldt0(sdtasdt0(xp,sz10),xp) ),
inference(superposition,[status(thm)],[c112,d24]) ).
cnf(d26,plain,
( xk = sdtsldt0(xp,xp)
| xk = sz00 ),
inference(demodulation,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( xk = sz00
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| xp = sdtasdt0(xp,X0)
| xp = sz00
| X0 != xk ),
inference(superposition,[status(thm)],[d26,c51]) ).
cnf(d28,plain,
( ~ doDivides0(xp,xp)
| xk = sz00
| xp = sdtasdt0(xp,X0)
| xp = sz00
| X0 != xk ),
inference(resolution,[status(thm)],[c72,d27]) ).
cnf(d29,plain,
( ~ doDivides0(xp,xp)
| xk = sz00
| xp = sdtasdt0(xp,X0)
| X0 != xk ),
inference(resolution,[status(thm)],[c89,d28]) ).
cnf(d30,plain,
( ~ doDivides0(xp,xp)
| xk = sz00
| xp = sdtasdt0(xp,xk) ),
inference(equality_resolution,[status(thm)],[d29]) ).
cnf(d31,plain,
doDivides0(xp,sdtasdt0(xp,sK99)),
inference(demodulation,[status(thm)],[c96,c95]) ).
cnf(d32,plain,
doDivides0(xp,sdtasdt0(xp,xk)),
inference(demodulation,[status(thm)],[d31,d2]) ).
cnf(d33,plain,
( xk = sz00
| doDivides0(xp,sdtasdt0(xp,sz10)) ),
inference(superposition,[status(thm)],[c112,d32]) ).
cnf(d34,plain,
( doDivides0(xp,xp)
| xk = sz00 ),
inference(demodulation,[status(thm)],[d33,d23]) ).
cnf(d35,plain,
( xk = sz00
| xp = sdtasdt0(xp,xk)
| xk = sz00 ),
inference(resolution,[status(thm)],[d34,d30]) ).
cnf(d36,plain,
( xk = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xp,xk)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[d35,d22]) ).
cnf(d37,plain,
( xk = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,sdtasdt0(xp,xk))) ),
inference(resolution,[status(thm)],[c72,d36]) ).
cnf(d38,plain,
( xk = sz00
| xk = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xp,sK61(xp,xp)) ),
inference(superposition,[status(thm)],[d35,d37]) ).
cnf(d39,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| xp = sdtasdt0(xp,sK61(xp,xp))
| xk = sz00 ),
inference(resolution,[status(thm)],[d34,c48]) ).
cnf(d40,plain,
( xk = sz00
| xp = sdtasdt0(xp,sK61(xp,xp)) ),
inference(resolution,[status(thm)],[c72,d39]) ).
cnf(d41,plain,
( xk = sz00
| xk = sz00
| sdtasdt0(xp,xk) = xp ),
inference(superposition,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
( xk = sz00
| xn = sz10
| xp != xp ),
inference(superposition,[status(thm)],[d41,d17]) ).
cnf(d43,plain,
( xk = sz00
| xn = sz10 ),
inference(equality_resolution,[status(thm)],[d42]) ).
cnf(d44,plain,
( xn = sz10
| sdtasdt0(xp,sz00) != sz00 ),
inference(superposition,[status(thm)],[d43,d12]) ).
cnf(d45,plain,
( xn = sz10
| sz00 != sz00 ),
inference(demodulation,[status(thm)],[d44,d1]) ).
cnf(d46,plain,
xn = sz10,
inference(equality_resolution,[status(thm)],[d45]) ).
cnf(d47,plain,
sdtasdt0(sz10,xm) = sdtasdt0(xp,xk),
inference(demodulation,[status(thm)],[c110,d46]) ).
cnf(d48,plain,
xm = sdtasdt0(xp,xk),
inference(demodulation,[status(thm)],[d47,d0]) ).
cnf(d49,plain,
( ~ aNaturalNumber0(sK99)
| xm != sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[d2,c115]) ).
cnf(d50,plain,
xm != sdtasdt0(xp,xk),
inference(resolution,[status(thm)],[c94,d49]) ).
cnf(d51,plain,
$false,
inference(resolution,[status(thm)],[d50,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n007.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.40 % WCLimit : 300
% 0.10/10.40 % DateTime : Sat Sep 26 02:58:04 UTC 2026
% 0.13/10.40 % CPUTime :
% 0.13/10.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.38/14.05 % SZS status Theorem for theBenchmark.p
% 28.38/14.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------